Question:medium

The magnetic moment of electron due to orbital motion is proportional to
(\(n\) = principal quantum number)

Show Hint

Orbital magnetic moment equals e L / 2m, and L is n h over 2 pi.
Updated On: Oct 1, 2026
  • \(n\)
  • \(n^2\)
  • \(\frac{1}{n}\)
  • \(\frac{1}{n^2}\)
Show Solution

The Correct Option is A

Solution and Explanation

Step 1: Current loop
$\mu = IA$ with $I = \dfrac{ev}{2\pi r}$ and $A = \pi r^2$, so $\mu = \dfrac{evr}{2}$.

Step 2: Bohr condition
$mvr = \dfrac{nh}{2\pi}$ means $vr = \dfrac{nh}{2\pi m}$.

Step 3: Combine
$\mu = \dfrac{e}{2}\cdot\dfrac{nh}{2\pi m} = \dfrac{neh}{4\pi m}$.

Step 4: Result
$\mu \propto n$, option (A). Quantities that go as $n^2$ or $1/n$ are the radius and speed in the Bohr model, not the magnetic moment.

Final Answer:
The magnetic moment is proportional to n. This is option (A). \[ \boxed{\text{(A) }n} \]
Was this answer helpful?
0